The marketing research department for the company that manufactures and sells “notebook” computers established the following price – demand function:
ters established the following price – demand function:
p(x) = 10 – 0,001x, where p(x) is the wholesale price in dollars at which x thousand computers can be sold.
Total cost (in dollars) of producing x items is given by C(x) = 7000 + 2x.
A) Find the revenue function and state its domain.
B) Find the marginal revenue function. Find R´(4000) and R´(6000). Interpret the results.
C) Evaluate the approximate revenue and exact revenue of producing 101-th notebook.
D) Find the profit function
E) Find the marginal profit function.
F) Evaluate the approximate profit and exact profit of producing 101-th notebook.
G) Find P´(5000) and P´(7000). Interpret the results.
4.The cost of gym membership, C, in Australian dollars (AUD), in Paolo’s Gym can
be modelled by the function
C = 65t
C = 65t + 30
where t is the time in months.
(a) Calculate the gym membership cost over a six month period.
(b) Sketch the graph of the function C = 65t + 30 for t ≥ 0.
(c) Calculate the time, t, in months, when the total cost reaches 290 AUD.
In the neighbouring Nicolo’s Gym, the initial payment is 75 AUD higher than in
Paolo’s Gym, however the monthly fee is lower at 30 AUD per month.
(d) Determine the number of months it takes for the total cost to be less by
attending Nicolo’s Gym in comparison to Paolo’s Gym.
6.I have a query, can you solve?
1. Sunshine Desserts sell 3 different flavours of exotic Ice-cream (Lychee surprise, Kumquat ripple and
(Lychee surprise, Kumquat ripple and Avocado 99). Three salespersons Joan, David and Tony each sold the following units, in 100 litre tubs, as shown below
Lychee surprise Kumquat Ripple Avocado 99
Joan 12 10 20
David 16 12 8
Tony 20 16 10
The total sales of each salesperson were £9,800, £8000, and £10,300 respectively. Calculate the cost of each type of ice-cream.